Complex Dynamics in the Kummer-Olsen Model of Calcium Oscillations

Zheng Fei Wu; Yi Zhou

doi:10.4028/www.scientific.net/AMM.226-228.505

Paper Titles

Analysis of Bearing Loads for Scroll Compressor Considering Phase-Angled Counterweights
p.483

The Research of Cylindrical Noise Source Distribution Using Near-Field High-Resolution Location Methods Based on MVDR Algorithm
p.487

The Near-Field Correction Method of the Basic Array Error Based on a Single Auxiliary Vector Hydrophone
p.493

Aeroelastic-Acoustics Numerical Simulation Research
p.500

Complex Dynamics in the Kummer-Olsen Model of Calcium Oscillations
p.505

Hopf Bifurcation and Numerical Simulation in a Calcium Oscillation Model
p.510

Analysis of Attitude and Dynamics Characteristic of a Kind of Submerged Buoy
p.516

Dynamical Analysis of a Calcium Oscillation Model in Non-Excitable Cells
p.521

Simulation Research on Defects Detection in Straight Pipes Using Guided Waves
p.526

HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vols. 226-228Complex Dynamics in the Kummer-Olsen Model of...

Complex Dynamics in the Kummer-Olsen Model of Calcium Oscillations

Abstract:

Oscillations of cytosolic calcium concentration, known as calcium oscillations, play a vital role in providing the intracellular signalling. These oscillations are explained with a model based on calcium-induced calcium release (CICR). The nonlinear dynamics of the Kummer-Olsen calcium oscillation model is discussed by using the center manifold theorem and bifurcation theory, including the variation in classification and stability of equilibria with parameter value. It is concluded that the appearance and disappearance of calcium oscillations in this system is due to supercritical Hopf bifurcation of equilibria. Finally, numerical simulations are carried out to support the theoretical analysis of the research. By combining the existing numerical results with the theoretical analysis results in this paper, a complete description of the dynamics of the Kummer-Olsen calcium oscillation model has now been obtained.

You might also be interested in these eBooks

Vibration, Structural Engineering and Measurement II

View Preview

Info:

Periodical:

Applied Mechanics and Materials (Volumes 226-228)

Pages:

505-509

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.226-228.505

Citation:

Cite this paper

Online since:

November 2012

Authors:

Zheng Fei Wu, Yi Zhou

Keywords:

Calcium Oscillation, Center Manifold, Supercritical Hopf Bifurcation

Export:

RIS, BibTeX

Price:

Permissions CCC:

Request Permissions

Permissions PLS:

Request Permissions

Сopyright:

Citation:

References

[1] J. Sneyd: Scholarpedia, Vol. 3 (2007) No. 2, p.1576.

Google Scholar

[2] M.J. Berridge, M.D. Bootman, and P. Lipp: Nature, Vol. 6703 (1998) No. 395, p.645.

Google Scholar

[3] U. Kummer, L.F. Olsen, C.J. Dixon, A.K. Green, E. Borhberg-Bauer and G. Baier: Biophys, Vol. 79 (2000) No. 11, p.88.

Google Scholar

[4] M. Perc and M. Marhl: Chaos, Solitions and Fractals, Vol. 18 (2003) No. 4, p.759.

Google Scholar

[5] L.J. Zhang, J. Wang and Y. Chang: Journal of Beijing University of Chemical Technology (Natural Science), Vol. 35 (2008) No. 3, p.104. (In Chinese).

Google Scholar

[6] Z.J. Jing, Y. Chang and G.R. Chen: Chaos, Solitons and Fractals, Vol. 22 (2004) No. 4, p.831.

Google Scholar

[7] S. Wiggins: Introduction to Applied Nonlinear Dynamical Systems and Chaos. (Springer, Germany 1990), p.5.

Google Scholar